Investigating the ground-state rotamers of n-propylperoxy radical Free

Low-temperature combustion occurs between 600 and 900 K,^1,2 and is comprised of cool flame oscillations involving free radical pathways. In this temperature regime, the barrierless, exothermic reaction between alkyl radicals and molecular oxygen³ strongly influences combustion dynamics. At this point, several subsequent reactions can proceed through energetically submerged transition states with respect to the initial reactants. The fate of alkylperoxy radicals is dependent on temperature, pressure, and the alkyl chain length (C_nH_2n+1) among other factors. This diverse chemistry was reviewed by Zádor, Taatjes, and Fernandes in 2011.⁴ For species with n ≤ 2 the reaction products are dominated by the concerted elimination of hydroperoxy radical (HOO^•) and formation of hydroxyl radicals (^•OH), the species believed to be the key to low-temperature combustion. Note that at elevated temperatures, the kinetic rate for the reverse reaction (ROO^• → R^• + O₂) becomes non-negligible due to its barrierless nature. This leads to what is call the “Negative Temperature Coefficient” (NTC) region where increasing temperatures counterintuitively lead to a delay in combustion.^5–8 

In this work, we consider the n-propylperoxy radical (n = 3).^8–12 This molecule is often considered to be an ideal combustion compound for theoretical examination because of its manageable size coupled with a combustion mechanism containing intermediates of interest. The most crucial propylperoxy intermediate^6,13,14 is formed by way of an internal hydrogen abstraction. This process occurs through a ring-like transition state, resulting in a carbon centered radical, often denoted as QOOH. Until recently,¹⁵ no QOOH species had been directly characterized, though the existence of these combustion intermediates has been included in most kinetic models.¹⁶ The difficulty in achieving this feat is due to the highly-transient nature of these intermediates. A 5- and a 6-membered ring transition state are available to n-propylperoxy radical for the formation of QOOH. The barriers corresponding to both ringed species lie lower in energy than reactants. While it is true that the six-membered ring transition state lies lower in energy than the 5-membered ring,^10,13,17 both are considered integral to the kinetic model of n-propylperoxy combustion. The QOOH species can undergo a second addition of molecular oxygen to form a peroxyalkylhydroperoxy radical (^•OOQOOH). The kinetics of the formation and decomposition of this combustion species has become of interest recently.¹⁸ The decomposition of ^•OOQOOH intermediate is believed to result in an increase in the number of radicals present in a combustion system. It is the increase in total number of radicals, in particular hydroxyl radicals, that leads to propagation and sustained low-temperature ignition. Since the n-propylperoxy radical system is the smallest system that can achieve the transition state of interest in route to the QOOH intermediate, it provides a unique opportunity for investigation using high-level theory. The knowledge gained by studying this relatively simple system can then be applied to much larger systems which are more prevalent within actual combustion models.

It is possible that under the right conditions, the n-propylperoxy radical species can relax into a deep potential well that is roughly 30 kcal mol⁻¹ below that of the reactants in lieu of continuing through the available combustion pathways. The focus of this paper is to investigate what happens to the radical species once it can be found in this well.

The n-propylperoxy radical contains three degrees of freedom with regard to dihedral angles, two of which are considered to be of greater importance the third less so. The dihedral that is often of least interest involves the rotation of the terminal methyl group of the molecule. The other two dihedrals are the ∠OOCC and the ∠OCCC. If one of these angles has a value of 180°, it is described as trans, whereas if the value of the dihedral is roughly ±60°, it is described as gauche. There are five rotamers, isomers due to rotation, that can be formed through combinations of these two dihedrals angles. The common naming system for these rotamers is to describe the ∠OOCC first and the ∠OCCC second. The only rotamer of the five with any symmetry is the trans-trans (TT) rotamer which has C_s symmetry. There also exist trans-gauche (TG) and gauche-trans (GT), which are both C₁ structures. The last two rotamers both contain two gauche dihedral angles, made distinct by the fact that the gauche-gauche (GG) rotamer contains dihedrals of the same sign while the gauche′-gauche (G′G) structure has dihedrals of opposite sign.

As the n-propylperoxy radical has gained scientific attention, it has been the interest of several different theoretical studies. A 2005 study by Merle et al. considered the rotamers on the ground state potential energy surface and found their relative energies to lie within one kcal mol⁻¹ at the CBS-QB3 level of theory. They also reported a population analysis using a Boltzmann distribution at 298 K. What Hadad and co-workers found at three different levels of theory was that all five of these ground state rotamers made up a significant portion of the population at 298 K. This suggests that, if observed, a sample of this radical species would likely contain a mixture of all five of the rotamers being studied.¹⁷ 

The 2005 study of Tarczay, Zalyubovsky, and Miller¹⁹ also included a theoretical investigation of the five rotamers. They also found the rotamers to lie very close in energy. At their “best” level of theory (G2) they found the energies of the conformers to be within 180 cm⁻¹ of each other. Along with this analysis they also used the equation of motion coupled-cluster with single and double excitations (EOM-CCSD) method to compute the Ã← X˜ excitation energy for each rotamer. The theoretical results were compared to experimentally obtained spectra from the same group.²⁰ The spectra used for experimental comparison were obtained using cavity ringdown spectroscopy (CRDS) which allows for the observation of these non-intense transitions. Matching their theoretical results with experimental results, they were able to reasonably label the excitation peaks from the CRDS spectrum with three of the five rotamers. A last piece of interesting analysis was done to determine barriers of rotation between each of the rotamers. With the B3LYP/6-31 + G^∗ method, the two different dihedral angles were scanned (0° to 180° for ∠OOCC and 0° to 360° for ∠CCCO). The results showed that the maximum barrier heights between any of the rotamers was approximately 1000 cm⁻¹ (∼2.86 kcal mol⁻¹). As they state in the paper, this relatively low barrier supports the notion that each of these rotamers would exist in equilibrium with one another at 298 K.¹⁹ One would also expect this to be true at combustion temperatures.

Some of the first spectroscopy done on peroxy radicals was done with UV absorption spectroscopy. The n-propylperoxy radical was studied with this method.²¹ However, this method does not allow for the mass specific study of peroxy radicals. The UV absorption studied corresponds to the B˜← X˜ transition which is a dissociative absorption. This absorption is not strongly dependent upon the non-peroxy moiety. Thus it is an effective way to determine the presence, but not identity of peroxy radicals. The advent of CRDS has greatly aided the study of peroxy radicals by increasing the sensitivity of measurements within the IR region. This method has been successfully applied to n-propylperoxy radical in order to study the Ã← X˜ transition.^20,22

To date, experimental spectra have not been reported which allow the resolution of fundamental vibrational transitions for this system. In light of this, we have predicted harmonic vibrational frequencies for the n-propylperoxy radical along with anharmonic corrections using second-order vibrational perturbation theory (VPT2). The fundamental frequencies reported in this paper should aid in the assignment of experimentally obtained vibrational spectra. This interplay of theory and experiment is well precedented within the field of peroxy radicals and related combustion species.^23–26 We seek to provide spectroscopic information in-line with this precedent for n-propylperoxy radical. Our analysis should aid in the spectral identification of this molecule from experimental studies. Further, an attempt to differentiate the rotamers and provide a method of specific rotamer detection may allow for the determination of the conformational make-up of this species within combustion systems. This would provide insight into the effect of rotamer populations on low-temperature combustion phenomena.

The reference geometry of each rotamer was optimized by using coupled-cluster theory, incorporating single, double, and perturbative triple excitations [CCSD(T)] with the Atomic Natural Orbital (ANO) basis set proposed by Almlöf and Taylor.²⁷ All geometry optimizations were completed with an unrestricted Hartree–Fock (UHF) reference along with a frozen core (1s-like molecular orbitals of carbon and oxygen) approximation.²⁸ The ANO family of basis sets was chosen because it appears to perform well within VPT2 theory when compared to similarly sized basis sets.²⁹ Given the relatively large system being studied, the ANO0 basis set (comparative in size to the Dunning cc-pVDZ basis set) made computations of anharmonic frequencies feasible. Initial harmonic frequencies were checked to make sure that no imaginary frequencies existed, ensuring that we had optimized to a true minimum on the potential energy surface in the case of each rotamer.

Anharmonic corrections to the potential energy surface for each rotamer were accounted for using second-order vibrational perturbation theory (VPT2) at the UHF-CCSD(T)/ANO0 level of theory. The full cubic force field was obtained along with the semi-diagonal portion of the quartic force field. These were obtained by numerical differentiation of analytic second derivatives. The CFOUR program was utilized for all computations.³⁰ 

In the case of resonances between a vibration and a single overtone, resonances were dealt with by building 2 × 2 matrices with anharmonic frequencies on the diagonal with cubic force-constants making up the off-diagonal elements. By diagonalizing these matrices, corrections to the computed anharmonic frequencies were obtained. In the case of both the GG and G′G rotamers, a single fundamental frequency was found to be in resonance with two different overtones. This required the building of a 3 × 3 matrix with cubic force constants between the fundamental frequency with each of the overtones and Darling–Dennison coefficients representing the interactions between the overtones. The process of identifying these resonances was done using the PyVPT2 program.³¹ 

Accurate relative energies for the rotamers were determined using the focal point analysis technique,^32–34 making use of the reference geometries at the UHF-CCSD(T)/ANO0 level of theory. Extrapolation to the complete basis set limit was done for both Hartree–Fock (HF) energies (three point extrapolation) and correlation energies (two point extrapolation) obtained using the Dunning correlation consistent cc-pVXZ (X = T, Q, 5) basis sets³⁵ via the following extrapolation functions:^36,37

and

Included in the analyses were high level correlation computations through coupled cluster theory including single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. These CCSDT(Q) computations were done using the MRCC code of Kállay interfaced with CFOUR.^38,39 In order to correct for the frozen-core approximation that was used during the single point energy computations, an auxiliary core correlation correction (Δ_core) was computed. This correction represents the difference between all-electron (AE) and frozen core (FC) single point energies that were computed using the Dunning correlation consistent triple-zeta basis set including core functions (cc-pCVTZ),

Also included in the corrections were anharmonic zero point vibrational energy corrections (Δ_{AZPV E}). In each case, this correction was obtained during the computations to determine the anharmonicity of the potential energy surface. Due to the fact that our system contains a relatively large number of hydrogens, we had to consider the possibility of non-adiabatic effects. In order to assure that we have a high level of reliability with regard to such effects, diagonal Born-Oppenheimer corrections (Δ_DBOC) were predicted at the HF/cc-pVTZ level of theory.^40,41 Final corrections were added to our results to account for relativistic effects (Δ_rel). These relativistic corrections were obtained by adding the mass-velocity and Darwin one-electron terms computed with the AE-CCSD(T)/cc-pVTZ method.^42,43

As one last piece of analysis, the vibrationally averaged equilibrium parameters (r_{g,0 K}) were computed and compared to the equilibrium internuclear distances (r_e). These results are reported in Table VI. Following the example of Copan, Schaefer, and Agarwal,²⁴ the vibrationally averaged bond lengths are obtained through the following Taylor expansion of the bond lengths in terms of normal modes of vibration,

We present our anharmonic vibrational frequencies for all five rotamers in Table I. Each column contains the set of harmonic frequencies, anharmonic corrections, and final anharmonic fundamental frequencies for a particular structure. It is worth noting that we do not follow the standard convention in our designation of the frequencies for the symmetric TT rotamer. Given that the rotamer has C_s symmetry, convention would require us to report all a′ fundamentals followed by all a″ modes. For ease of comparison with our C₁ rotamers, which have no point group symmetry, we have more appropriately reported the fundamentals in decreasing order of frequency. Our harmonic frequencies show general agreement with previous research done on this system.¹⁷ The anharmonic corrections to these frequencies may be understood in terms of the primary bonds involved in each vibrational mode. Those vibrational frequencies which correspond to C–H bond stretches (modes 1–7) exhibit large anharmonic corrections, generally above 100 cm⁻¹ in magnitude. All other modes have anharmonic corrections that are below 50 cm⁻¹ in magnitude. Any resonances that were found between fundamentals and overtones were corrected for using the PyVPT2 program described in the theoretical methods section of this paper.³¹ Those frequencies which were subject to resonance are labeled within the tables, along with which overtone band(s) provide the resonance interaction.

Comparing vibrational frequencies between different rotamers is complicated by the lack of symmetry present in four of the five species studied. In Table II we have labeled some of the more recognizable frequencies. The easiest assignment to be made is that for the O–O stretch. For each rotamer, this is reported as ν₁₉. The frequencies we report for this mode are 1063 cm⁻¹ for the GG rotamer, 1060 cm⁻¹ for the GT, 1073 cm⁻¹ for the TG, 1064 cm⁻¹ for the G′G, and 1072 cm⁻¹ for the TT. These frequencies span a range of only 13 cm⁻¹. This comparison indicates that this mode is not largely dependent upon the alkyl portion of the molecule. As may be seen in Table II, these modes are among the most intensely IR active modes for each of the five rotamers. This fundamental should appear in any IR spectrum of the molecule. Unfortunately, except at very high resolution, this mode would not be a good candidate for differentiating the rotamers, due the fact that there is no large variation in this fundamental across the five rotamers.

The C–O stretching modes are similar to the O–O stretching modes in that the range of frequencies over which these modes occur is modest but more so than found for the O–O stretch. The fundamental band which primarily contains the C–O stretch is ν₂₁. From Table I, the reported fundamentals for this mode range from 908 to 953 cm⁻¹. The intensities associated with this mode fall in one of two camps, where the intensities reported for the TG, TT, and G′ G rotamers are approximately twice the intensities reported for the GT and GG rotamers. With all of this in mind, it may be possible to specifically detect the TT rotamer [ν(CC) = 953 cm⁻¹ ] which has a favorable combination of high IR intensity and distinct frequency. For the other rotamers, any unresolved spectrum might not be helpful for rotamer specific detection.

The two C–C bond stretching modes offer the best hope for rotamer specification. The modes involving these two stretches are ν₁₃ for the C_α–C_β stretch and ν₁₂ for the C_β–C_γ stretch. Combining the analysis of these two modes is much more useful in this case than looking at them individually. The most distinct of the rotamers is likely the higher energy (by only 0.5 kcal mol⁻¹) G′ G rotamer. From Table II, it can be seen that only ν₁₃ is predicted to appear as a fairly strong peak within an IR spectrum, while for the other C–C stretching mode ν₁₂, the IR intensity is small (0.7 km mol⁻¹). The TG rotamer essentially shares the same frequencies for both modes with differences of 3 cm⁻¹ and 5 cm⁻¹ for ν₁₂ and ν₁₃, respectively. The differentiating factor between the G′ G and TG rotamers comes with their relative frequencies. By comparison with the strong O–O stretch (intensities 19–28 km mol⁻¹), the ν₁₃ C_α–C_β intensity for the G′ G rotamer is about half as intense, while the ν₁₃ intensity for the TG rotamer is only about one fifth as intense. In this way, these two rotamers may be differentiated from one another and are distinct enough from the other rotamers that a well resolved experimental spectrum might be able to distinguish either the G′ G or the TG from the other rotamers. The TT rotamer is the next most easily identifiable rotamer. From Table II, the frequencies for the two C–C modes are essentially identical, differing by 2 cm⁻¹, and should appear as one, fairly intense peak, particularly in matrix isolation. The last two rotamers, the GT and GG, present a challenge for this combined analysis. Neither of these two rotamers is predicted to have an intense band for either of these modes. Further, the frequencies for the modes of interest only differ by 5 cm⁻¹ and 10 cm⁻¹. This combined analysis, even appended with information from more modes, will have a difficult time differentiating these two rotamers from one another. Our global analysis of the C–C stretching modes, however, does get us closer to rotamer specific detection.

The lowest frequency torsion modes within each of the conformers have also been assigned. In four of our five rotamers, we find that the lowest frequency mode largely involves the torsion about the ∠OOCC dihedral angle. The exception is the GT conformer where this torsion is assigned to ν₂. The fundamental frequencies for this mode lie between 69 and 113 cm⁻¹, most of which fall in the lower end of this range. Considering the ∠OCCC dihedral, we find that the torsional motion involving this dihedral can be assigned to ν₂, again the exception being the GT rotamer. The frequencies for this motion lie between 98 and 145 cm⁻¹. The last dihedral degree of freedom involving the terminal methyl group can generally be assigned to ν₃ with the exception of the TT rotamer where ν₄ is assigned to this mode. The frequencies assigned to terminal methyl rotation range from 173 to 227 cm⁻¹. It is interesting to note that the theoretical frequencies span a range of 54 cm⁻¹. A slight dependence upon the OOCC dihedral angle can be observed. Rotamers with a gauche dihedral angle at this position have higher frequencies corresponding to terminal methyl rotation, while those rotamers with a trans dihedral at this position have lower frequencies. Given the slight dependence upon the OOCC dihedral angle on the torsional modes a future avenue of study presents itself. A coupled rotor analysis of the torsional modes can be performed to project out their effect on the remaining vibrational modes. Tarczay and co-workers¹⁹ predicted rotational barriers of roughly 250–1000 cm⁻¹ associated with transformations between rotamers of the n-propylperoxy radical, and we find the barrier for terminal methyl rotation to be roughly 900 cm⁻¹ using B3LYP and a triple-ζ quality basis set. Given that the rotational barriers within the n-propylperoxy radical are of this magnitude, we are confident that VPT2 can offer a valid treatment of these modes.

As noted in Table I, each rotamer shows a resonance between one of the C–H stretching fundamentals and at least one overtone band. All of the resonances observed are between fundamental C–H stretching modes and first overtones of ∠HCH bends. For both the GG and G′ G rotamers, a single C–H stretching fundamental (ν₇ for GG and ν₆ for G′ G) is in resonance with two separate ∠HCH bending overtones (ν₈ and ν₉). All of the modes associated with these frequencies involve the terminal methyl group. These resonances require the building of 3 × 3 contact matrices in order to be resolved. The corrections for these resonances were +36 cm⁻¹ in each case. For the TG rotamer, there is found a fundamental which suffers from resonance with a single overtone. This resonance also occurs between the fundamental involving the terminal C–H stretch (ν₇) and a terminal methyl ∠HCH bend (ν₈). The applied correction was 14 cm⁻¹, much smaller than that for the GG and G′ G resonances. This is likely due to the fact that the resonance only involves a single overtone instead of two.

The remaining pair of rotamers, GT and TT, suffer from two separate resonances between a single C–H stretch and a single ∠HCH bend. The first of these resonances occurs between the ν₆ stretch and the ν₈ bend for each rotamer. Both of these modes involve the C_βH₂ group of the molecule. This resonance is in contrast to the GG and G′ G rotamers which only display resonances involving the terminal methyl moiety. The second pair of resonances do involve the terminal methyl group. These occur between the ν₇ stretching and the ν₉ bending modes. The corrections applied to account for both of these resonances were roughly the same as that for the TG. This is likely due to the fact that each interaction accounted for was between a single fundamental and a single overtone. All of the resonances discussed within this section have been noted in Table I along with identification of which fundamentals and overtones participate in each resonance. Specific values for the applied corrections along with cubic force constants associated with resonances have been included in the supplementary material for this paper. A potential dependence upon the ∠OCCC dihedral angle might be inferred from these observations. Further study would be required to draw conclusions based upon the ∠OCCC dihedral angle (or terminal ∠CCCC dihedral angle in any larger alkylperoxy molecule) and its effect upon the types of resonances that plague a particular alkylperoxy IR spectrum.

The focal point results provide definitive results concerning the relative energies of the different rotamers. The GG conformer lies lowest in energy. For each of the conformers, we have computed correlation corrections through CCSDT(Q). In every case, our results show good convergence at this level of correlation with the largest difference between CCSDT/cc-pVDZ and CCSDT(Q)/ cc-pVDZ being 0.02 kcal mol⁻¹. None of the relative corrections for core-correlation, zero-point vibrational energy, or relativistic effects is larger than 0.01 kcal mol⁻¹, and most often these should be considered to be nearly nil, given the numerical precision associated with these results.

Considering the other computed energetic corrections evaluated here, it may be seen that the system is fairly well behaved. Neither the core-correlation nor the DBOC corrections significantly adjust our predictions at the precision of 0.01 kcal mol⁻¹. The largest correction predicted was the AZPVE correction obtained from the anharmonic corrections to the potential energy surface. The AZPVE correction for the lowest energy conformer (GG) is 62.19 kcal mol⁻¹ (∼21 750 cm⁻¹) and the AZPVE values reported in the focal point tables are relative to this. AZPVE serves to further distance our higher energy rotamers from the GG rotamer by 0.07 kcal mol⁻¹ in the case of the TG rotamer and 0.08 kcal mol⁻¹ in the case of the TT rotamer. The corrections themselves can be found in the reported focal point analysis tables (Tables III–VI).

The equilibrium geometries reported were all obtained at the ANO0/CCSD(T) level of theory. A strict convergence criterium (RMS force gradient ≤10⁻⁶) was required to ensure that the geometries obtained were precise. The expectation of the spin-squared operator was found in each case to ensure that spin-contamination was not greatly affecting our data. In every case, the expectation value was between 0.7611 and 0.7618. This can be compared to the ideal value of 0.75 for any doublet electronic state. This good agreement gives further confidence in the validity of the present theoretical predictions.

Examining the geometries of all five rotamers, one can see that they are reasonably consistent. Comparing the O–O bond length present in the peroxy moiety, one finds little difference. These bond lengths differ between 1.344 and 1.346 Å for the five rotamers. The C–O bond distances show roughly the same amount of variance. These C–O bond distances fall between 1.458 and 1.461 Å. The reported C_α–C_β equilibrium bond distances only range from 1.523 to 1.526 Å. Likewise, the reported C_β–C_γ equilibrium bond lengths lie between 1.535 and 1.536 Å. Much like their energies, the rotamers are similar with regard to the bond distances between backbone atoms. The angles within all five rotamers are also reasonably similar to one another. Figure 1 contains representations for all of the rotamers for general comparison of geometries. Figure 2 shows the equilibrium structure of the lowest energy rotamer with bond distances and angles labeled.

Because the rotamers are defined in terms of dihedrals, Newman projections for each of the rotamers have been provided (Figure 3) in order to explicitly represent the dihedral angles of interest. Note that the molecules do not always adhere to the intuitive 60° gauche dihedral and 180°  trans dihedral. One particular offender is the G′G rotamer whose OOCC dihedral is closer to 90° than either of the idealized dihedrals.

The effects of vibrational averaging are reported in Table VII. As can be seen from the table, the vibrational averaging leads to an increase in bond distances in every case. As the molecule vibrates, the nuclei are on average further from one anther. The greatest corrections for vibrational averaging occur for bonds between carbon and hydrogen. This reflects the fact that these C–H bonds which contain the lightest element will undergo relatively large amplitude vibrations. These corrections are very systematic and lie between 0.0214 and 0.0221 Å. Heavier nuclei generally undergo smaller amplitude vibrations. Thus, bond lengths involving these heavier atoms, carbon and oxygen in the case of the n-propylperoxy radical, experience smaller corrections when vibrationally averaged. The smallest corrections observed were found in the distance of the O–O bond. Given that the heaviest element present in the n-propylperoxy radical is oxygen, this is our most massive bond. The corrections for the O–O bond distance lie between 0.0065 and 0.0068 Å, a full order of magnitude below the corrections for the C–H bond distances. These results support the notion that internuclear distances involving bonds between heavier atoms will see smaller vibrationally averaged corrections than those of bonds involving light atoms such as hydrogen.

The five ground state rotamers of the n-propylperoxy radical have been studied using high-level ab initio methods. Structures for all five of the rotamers are reported with coupled cluster theory. Geometries for all five rotamers are compared to one another and found to be similar with the exception of the characteristic dihedral angles of these rotamers. Vibrationally corrected bond lengths utilizing the cubic force constants obtained during anharmonic VPT2 computations are also reported. In every case, zero-point vibrations lead to extended bond lengths. The amount of this vibrational extension is related to the anharmonicity experienced by the vibrational modes involving the stretching of these bonds. The C–H bonds, whose bond stretching modes have anharmonic corrections of roughly 150 cm⁻¹, experience the greatest degree of extension while the smallest extensions are reported for the O–O bonds whose anharmonic corrections are between 29 and 35 cm⁻¹.

Accurate relative single-point energies at the CCSDT(Q)/ CBS level of theory are reported for each of the rotamers by use of the focal point approach. The lowest energy rotamer is found to be the GG rotamer, followed by the GT, TG, TT, and G′ G rotamers, respectively. The resulting energies, much like the structures, are similar. The reported energies suggest that any population of the n-propylperoxy radical would likely contain a mixture of all five rotamers. This mixing of energetically close states leads to difficulty in rotamer specific spectroscopic detection of the n-propylperoxy radical. In light of this, fundamental frequencies have been reported in order to assist with this difficult spectroscopic interrogation. With a goal of differentiating the spectra reported for the rotamers, analyses of both the frequencies and intensities of the fundamental vibrational modes were carried out. It is predicted that the most propitious way to specifically detect a given rotamer may be to analyze the C–C bond stretching modes, reported in Table I as ν₁₂ and ν₁₃, occurring near 1400 cm⁻¹. Even if this rotamer-specific detection is not achieved, advances in spectroscopy may soon be able to obtain a vibrationally resolved spectrum for the n-propylperoxy radical molecule. The spectroscopic predictions presented in this paper should aid in the assignment of such spectra.

The supplementary material includes structures, including cartesian coordinates for each of the rotamers. Also reported are harmonic and anharmonic corrections, and final anharmonic frequencies for each of the rotamers. Additionally, included is a description of the resonance corrections to certain frequencies within our analysis.

This research was supported by the Department of Energy, Basic Energy Sciences, Division of Chemical Sciences, Fundamental Interactions Team, Grant No. DEFG02-97-ER14748. We thank Dr. Jay Agarwal for the use of his PyVPT2 program.